MEASUREMENT OF HEIGHTS. 519 



vapours alters equally ^vith equal changes of temperature, and 

 that the alteration is proportional to degrees of the mercurial 

 thermometer. If the elasticity at the temperature of melting 

 ice be 1, and its alteration for a change of temperature corre- 

 sponding to one degree of the thermometric scale = k, its value 

 for a given amount of the thermometer is 



E = 1 + ^' /. 



For the temperature of boiling water Gay Lussac found E 

 = 1-375. 



Besides the three gases the atmosphere contains aqueous va- 

 pour, which is present in variable quantities, determinable only 

 by experiment in each particular case. I propose to return 

 hereafter to this part of the subject ; but I will first consider of 

 atmospheric air unmixed with aqueous vapour. 



2. 



Barometric measui'ements of height rest on a comparison of 

 the observed pressure of the atmosphere at different heights, 

 with the expression denoting the conditions of its equilibrium. 

 Although this expression has been developed in the Mecanique 

 Celeste, and in several subsequent works, I shall not omit its 

 development here ; as it will enable me to introduce a small 

 alteration, as well as to connect what I have further to say. 

 Mariotte's law requires that to produce equilibrium the density 

 (5) of the air should be in the direct ratio of the pressure [p) 

 which it experiences, and which it consequently exerts in 

 return, and in the inverse ratio of its elastic force ; or that 



8 . E 



be constant. The air is here supposed to be constituted 



alike at all altitudes. If we take for the measure oi p the 

 pressure exerted on an unit of surface, by a column of mercury 

 of .3.36-905 Parisian lines, at the temperature of melting ice, at the 

 surface of the earth in the latitude of 45°, — for the measure of S 

 the density of mercury at the temperature of melting ice, — and 

 for the measure of E the specific elastic force of air at the same 

 temperature, — and if we make 8 = D for j9 = 1, and E = 1, we 

 have 



8.E=;9D (3.) 



The pressure of the air at an elevation x above the surface of 

 the earth, or at a distance a + x from its centre, is the sum of 

 the pressures of all the strata above x, A stratum between the 



